Results 31 to 40 of about 9,324,703 (377)

A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms

Annales Mathematicae Silesianae, 2022
Let S be a semigroup, and let φ, ψ: S → S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f(xϕ(y))+f(ψ(y)x)=2f(x)f(y),      x,y ∈ S,
Akkaoui Ahmed, El Fatini Mohamed, Fadli Brahim   +2 more
doaj   +1 more source

QED in external fields, a functional point of view [PDF]

, 2001
A functional partial differential equation is set for the proper graphs generating functional of QED in external electromagnetic fields. This equation leads to the evolution of the proper graphs with the external field amplitude and the external field ...
C. J. Burden, C. J. Burden, D. Fliegner, D.-S. Lee, E. J. Ferrer, J. Alexandre, J. Alexandre, J. Schwinger, K. Farakos, L. D. Landau, L. F. Abbott, L. F. Abbott, V. P. Gusynin, V. P. Gusynin, V. Skalozub, W. Dittrich, W. Heisenberg   +16 more
core   +2 more sources

A Unifying Principle in the Theory of Modular Relations

Mathematics, 2023
The Voronoĭ summation formula is known to be equivalent to the functional equation for the square of the Riemann zeta function in case the function in question is the Mellin tranform of a suitable function.
Guodong Liu, Kalyan Chakraborty, Shigeru Kanemitsu   +2 more
doaj   +1 more source

Dynamics of the Universal Confining String Theory on the Loop Space [PDF]

, 1997
Starting with the representation of the Wilson average in the Euclidean 4D compact QED as a partition function of the Universal Confining String Theory, we derive for it the corresponding loop equation, alternative to the familiar one.
Antonov, D. V.
core   +2 more sources

Axiomatic Characterizations of Information Measures

Entropy, 2008
Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measures. (
Imre Csiszár
doaj   +1 more source

Numerical Calculations to Grasp a Mathematical Issue Such as the Riemann Hypothesis

Information, 2020
This article presents the use of data processing to apprehend mathematical questions such as the Riemann Hypothesis (RH) by numerical calculation. Calculations are performed alongside graphs of the argument of the complex numbers ζ ( x + i y ...
Michel Riguidel
doaj   +1 more source

Hyperstability of general linear functional equation

Aequationes Mathematicae, 2016
Our purpose is to investigate criteria for hyperstability of linear type functional equations. We prove that a function satisfying the equation approximately in some sense, must be a solution of it.
A. Bahyrycz, J. Olko
semanticscholar   +1 more source

A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei

, 2003
A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei.
Adcox, Adcox, Adler, Adler, Adloff, Adloff, Ayala, Ayala, Ayala, Back, Back, Back, Back, Back, Balitsky, Balitsky, Balitsky, Bartels, Bartels, Bartels, Bartels, Bartels, Bazilevsky, Bearden, Bearden, Breitweg, Breitweg, Chekanov, Collins, Dunlop, E. Levin, Eskola, Ewerz, Golec-Biernat, Golec-Biernat, Golec-Biernat, Golec-Biernat, Gotsman, Gotsman, Gotsman, Gribov, Iancu, Jalilian-Marian, Jalilian-Marian, Jalilian-Marian, Jalilian-Marian, Kharzeev, Kharzeev, Kharzeev, Kharzeev, Kovchegov, Kovchegov, Kovchegov, Kovchegov, Kovchegov, Kovner, Kowalski, Kuraev, Kwiecinski, Laenen, Levin, Levin, Levin, Lipatov, M. Lublinsky, McLerran, McLerran, McLerran, McLerran, McLerran, Milov, Mioduszewski, Mueller, Mueller, Mueller, Mueller, Mueller, Mueller, Munier, Munier, Sakaguci, Schwimmer, Stasto, Weigert, Xu   +84 more
core   +2 more sources

On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families

Mathematics, 2021
Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ ...
Shaul K. Bar-Lev
doaj   +1 more source

Functional evolution equations

Journal of Mathematical Analysis and Applications, 2003
The paper concerns the functional evolution equation \[ u'(t) \in B u + F(t, u_t) , \;\;t >0, \] \[ u_0(s)= \phi(s)\in C^1([-r,0];X), \] where \(X\) is a real Banach space, not necessarily reflexive, \(F : [0,\infty) \times C([-r,0];X) \to X \) is a single-valued function and \(B: D(B)\subset X \to X\) is a multi-valued nonlinear operator.
openaire   +2 more sources